Lorentz Jr

There's a distinction between flow of electrons and propagation of electromagnetic fields. Propagation of electromagnetic fields is at or near c. There's no distinction between flow of electrons and flow of charge (except for the multiplicative factor of e). EDIT: As Mordred mentions below, the multiplicative factor should be -e instead of +e.

Electrons have a lot of charge. It doesn't take much motion for them to create a moderate amount of current. I believe the signal about the motion travels through the electromagnetic field surrounding the wires at the speed of light. Electron drift velocity Youtube debate about current and fields

Interesting! I always thought action at a distance was just an assumption that Newton made to keep his theory as simple as possible, but it was sort of forced on him by Galilean relativity. A "true" Newtonian gravity could propagate at a finite speed, but only relative to a fixed reference frame. I never thought about that before. Einstein/Lorentz relativity is the only way to have both relativity and a finite propagation speed (i.e. a finite speed without a preferred frame). 🤔

Interesting. There doesn't seem to be an online repl anywhere. I thought there was, but that would have been back in the '00s. 😄 So you'll have to output values manually. The traditional functions are WRITE-LINE for simple output and FORMAT for pretty-printing. Only the most awesome computer programming language of the 1960s! 😋

It sounds like @Genady just means the solution applies for a central body of any mass. Planet, star, black hole, whatever. Not general in terms of initial conditions, but it's what the OP was asking about (clock C).

[math]\displaystyle{d\tau^2 = \rho dt^2 - \frac{dr^2}{\rho} - rd\phi^2}[/math] where c=1 and [math]\displaystyle{\rho \equiv \left(1-\frac{r_{\textrm{s}}}{r}\right)}[/math]. [math]\displaystyle{d\tau_A = \rho dt}[/math] [math]\displaystyle{d\tau_D^2 = \rho dt^2 - rd\phi^2 = \frac{d\tau_A^2}{\rho} - rd\phi^2 }[/math] [math]\displaystyle{\frac{d\tau_D^2}{d\tau_A^2} = \rho - \left(\frac{dr\phi}{d\tau_A}\right)^2}[/math] [math]\displaystyle{\sqrt{ \rho - v_{DA}^2}}[/math]

C will start out at the same rate as B, because both clocks are moving slowly and far away from Earth. From B's perspective, C will slow down as it falls, according to the Schwarzschild metric: [math]\displaystyle{c^2d\tau^{2}=c^2\left(1-\frac{r_{\textrm{s}}}{r}\right)dt^{2}-\left(1-\frac{r_{\textrm{s}}}{r}\right)^{-1}dr^{2}-r^{2} d\phi^{2}}[/math] (with thanks to @joigus for the TeX 🙂) dτ is called an object's "proper time". That's the amount of time that passes for A or C (from B's perspective) when a time dt passes for B (assuming B is moving slowly and is very far away). As you can see, the dr term is negative (because [math]r>r_s[/math]), so C will be running more slowly than A as it falls past A (because r is changing for C). The [math]d\phi[/math] term is also negative, so a clock D orbiting at the same altitude as A will also run more slowly (because [math]\phi[/math] is changing for D). C will be slower than D because (a) it's moving faster (more total energy - same potential = more kinetic, and the distance D travels is [math]ds = r d\phi[/math] < dr) and (b) the dr term has a larger coefficient than the [math](rd\phi)[/math] term.

[math]\displaystyle{d\tau^2 = \left( 1 - \frac{1}{r}\right)dt^2 - r^2 d\theta^2}[/math] [math]\displaystyle{c^2d\tau^{2}=c^2\left(1-\frac{r_{\textrm{s}}}{r}\right)dt^{2}-\left(1-\frac{r_{\textrm{s}}}{r}\right)^{-1}dr^{2}-r^{2}\sin^{2}\theta d\theta^{2}}[/math]

C vs A can sort of be verified (as long as C is slower). A clock falling from infinity moves faster in Earth's frame than one in circular orbit (more total energy + same potential = more kinetic), and they're both in free fall, so the falling clock must tick more slowly than the orbiting one when they're at the same altitude. And it might be possible to compare them directly by digging a tunnel through Earth so they cross paths again on the other side. Not very practical, of course.... And finally, the orbiting clock passes by the stationary clock periodically, so those two can be compared directly.

What I wonder about is a clock sitting just above the surface (with little or no rotation about the center of the planet) vs one in high-speed orbit just above the surface (in a vacuum). In terms of SR, the orbiting clock should be slower because it "moves" and accelerates* around the planet, but I'm afraid to guess when gravity is involved, and in GR it's the "stationary" clock that's accelerating! 😶 I guess C/orbiting would have to be slower than A/fixed, because C/orbiting is moving faster as seen by B/distant, which is at least close to inertial in both SR terms and GR terms. * Not literally because of the acceleration, but in SR, acceleration shows that the orbiting clock passes through multiple reference frames, as the astronaut and spaceship do in the twin paradox.

I think the idea @Genady was making is that Galilean gravity wouldn't (or wouldn't have to) be modeled as curvature of anything. It would (or could) just be a regular field in flat space, like the electric field. As I mentioned earlier, the whole point of spacetime and Einstein's work was to make the laws of dynamics and gravity consistent with (Lorentz-invariant) electrodynamics.

Right. So Lorentz invariance would be a (very strange) property of the ether (i.e. the vacuum), not a consequence of "geometry". That means it wouldn't necessarily apply to all natural phenomena, so there could be influences that propagate faster than light. Without an ether, the Galilean limit would be where c goes to infinity, which would mean ϵ0μ0=0 . So ϵ0 and/or μ0 would have to be zero. If ϵ0=0 , there would be no electric charge, and that means no magnetic field. So no electric or magnetic phenomena at all. If μ0=0 , Ampère's circuital law wouldn't exist. That's the one where the magnetic field is affected by electric currents and changing electric fields, so the magnetic field would always have to be zero (or maybe a uniform constant throughout all of space, in which case space wouldn't be isotropic, i.e. the magnetic field would define a special direction in the universe and electric charges would keep zooming around in circles and helical paths 😄).

As Genady said, gravity in a Galilean universe would look like Newtonian gravity, but I don't think there would be magnetic fields. Or at least they would be different. Maxwell's equations are Lorentz invariant (that was the whole motivation for Einstein's development of relativity in the first place), so their current form wouldn't be possible in a Galilean world.

Internal reflection inside the lens????? That still doesn't differentiate between the letters and the finger though.

Diffraction should move the image away from the obstacle, not toward it. (Also, I should have said "Diffraction" in my first post, not "Refraction". 🙄) Light that would have reached the observer in a straight line gets redirected, so the observer doesn't see it. What the observer sees is slightly less diffracted beams that don't pass quite so close to the obstacle.

I don't see the point of making expansive claims about things we can't see and hardly understand. Who knows what happens internally during particle interactions? Don't QFT calculations involve integrals over sets of physical trajectories?

Yes, I think so. I'm actually running into reproducibility problems (😡), maybe getting tired, I don't know. But it did work with an eraser, so I doubt it's air near the finger being heated. We'll see what the OP says. I seem to develop some kind of double vision when I blur my eyes, so there's a second image of the letter that shows "through" the sliver of one of the images of the object in front of it that sticks out past the other image. Sometimes the letter is skewed, sometimes it's not. It also seems to work with printed text on paper (although that's trickier because of shadows), so I guess it's not related to the phone screen.

This happens to me if I hold my phone close and let my eyes go out of focus. When I wear reading glasses and keep the letters in focus, it doesn't happen. And it happens to your camera too, so it sounds like distortion from the lens. But why does it only affect the letters and not the finger? Refraction should move the letters the other way, away from the finger. Very strange. Unless it really is some weird thing where the brain misinterprets the line of the letter when it's close to another edge and the image is fuzzy. It's not the angle though. at 0:17 and 0:19, the whole j and one whole side of the u move toward the finger.

... except when they're inventing new gists, which is what cults do. 😉

Minkowski and modern physicists have argued that space-time qualifies as "geometry" in some way that extends beyond mere mathematical abstraction (or at least that it's just as physically meaningful as Euclidean space). Sean Carroll and Lee Smolin have both said the way to "explain" relativity is to "change your intuition." I take this to mean accepting space-time as geometry, which has traditionally been defined as the study of physical objects. The OP's comment may not be literally correct, but I think that's the gist of it (i.e. the intuition that motivates it).

Depth psychologists tell us that most dreams have meaning on two or more levels simultaneously. Looking back on recurrent dreams I had during my younger years, they obviously represented my unconscious thoughts about important themes in my life at the time, and some individual dreams were just as obviously based at least in part on events of the previous day. The only examples of dreams representing responses to immediate stimuli while the dreamer is sleeping that I can think of would be this and this. And even those dreams obviously have additional significance to the dreamer at one or more deeper level(s). 😉

Clothing over smooth skin (A) is better than clothing over hairy skin (B). Clothing over hairy skin is better than no clothing at all (C). Not saying that's true, but A>B doesn't disprove B>C.

Right. And you proved that with your comment about the cars stopping simultaneously in the frame moving at the final speed vfinal relative to the tracks. Exactly. And therefore the ending solution in the vfinal frame must be the same as the beginning solution in the track frame, except the n's are reversed (n=0 at the front) and the formula applies to negative values of t (relative to the stopping time). Now write down that solution (it's in the "primed" frame) and transform it into the track frame to see what it looks like! 😋

Even if computers did have some kind of subjective experience (as in panpsychism), it would be very different from human experience. Something along the lines of "OMG THEY TURNED ON THE POWER AGAIN NOW I HAVE TO DO ANOTHER ONE OF THOSE STUPID SIMULATIONS CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG CHUG ..." And of course even that description anthropomorphizes computers too much. I can't imagine computers having any kind of subjective experience that even remotely resembles that of human beings.

It's relevant to the thread topic because the OP is concerned about not understanding subjective social phenomena. So the question is whether the thread itself belongs in a science forum. The OP mentioned various scientific issues in his post, but his primary concern seems to be perceptual.